We can represent the numbers in binary float point as

The binary point between the digits b0 and b1 does not exist physically in the computer. Simply, the logic circuits of the computer are designed such that the computations result in numbers that correspond to the assumed location of this point.

According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).

We can represent 5 as

For a two’s complement representation, the truncation error is always negative and falls in the range

(101.01)2=1*22+0*21+1*20+0*2-1+1*2-2=(5.25)10

According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).

The truncation error for the sign magnitude representation is symmetric about zero and falls in the range

Let us consider two numbers X=M.2E and Y=N.2F

The round-off error is independent of the type of fixed point representation. The maximum error that can be introduced through rounding is 0.5(2-b+2-bm) and this can be either positive or negative, depending on the value of x. Therefore, the round-off error is symmetric about zero and falls in the range